Welcome to the q-bio Summer School and Conference!


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This series of lectures and projects will be held at the new Fort Collins Colorado campus. We will explore stochasticity and cell-to-cell variability in the measurement and modeling of biochemical systems. In particular, we will concentrate on the effects that small numbers of important molecules (i.e. genes, RNA, and protein) have on the dynamics of living cells. We will review experimental manifestations of stochastic effects in molecular biology, as can be measured using single-cell and single-molecule techniques. We will discuss the most recent analytical and numerical methods that are used to model these systems and show how these methods can improve interpretation of experimental data. We will study how different cellular mechanisms control and/or exploit randomness in order to survive in uncertain environments. Similarly, we will explore how single-cell measurements of cell-to-cell variability can reveal more information about underlying cellular mechanisms.

This section of the summer school will include a number of instructor-suggested group projects, in which students will apply various numerical techniques to formulate, identify and solve stochastic models for gene regulatory systems. Students will then apply these tools to model experimental flow cytometry or other single-cell data. Access and knowledge of Matlab will be helpful, but is not strictly necessary.

This section of the summer school will be co-organized by Brian Munsky, Doug Shepherd, Sabrina Spencer. Please address all questions about this section of the summer school to an organizer.



Project Mentors

Course Materials


  • Introduction to Stochasticity. The importance of stochasticity in gene regulatory networks. Key examples from the literature.
  • Discussion of the importance of stochasticity in small populations. Stochastic Phenomena: switching, focusing, resonance, filtering.
  • The effects of positive and negative feedback.
  • The physics behind stochastic chemical kinetics.
  • Connection between deterministic and stochastic reaction rates.
  • Derivation of the Master Equation for discrete stochastic processes.
  • Solving the Chemical Master Equation: exact solutions for linear propensity functions,
  • Kinetic Monte Carlo algorithms: Gillespie algorithm, Tau Leaping. Chemical Langevin equation. Time separation schemes. Hybrid methods.
  • Density Computation Approaches: Finite State projections techniques, Moment Generating Function Techniques, Moment Closure Techniques, Fokker Planck equation.
  • Simplification of complex biochemical processes.
  • Switch rate analyses, waiting/completion times.
  • Single cell measurement techniques: flow cytometry, fluorescence microscopy, time lapse microscopy.
  • Using fluctuations to infer system mechanisms and parameters.
  • Markov Chain Monte Carlo methods.

Lectures and slides

  • To be announced


  • TBA


  • To be announced

Journal Club Readings

To be announced.

Group Projects

  • A variety of group projects will be proposed and discussed in the first few days of class. Projects are expected to last beyond the dates of the school and may result in a scientific publications. Projects will consider open problems in the integration of experimental and computational investigations of stochastic gene regulation. General research projects will include: single cell image processing, computational analysis of single cell and single molecule measurements, computer aided experiment selection, among others.